Some Results on Digital Chirp

Abstract

Generating chirp waveforms by means of phase coding yields a simple, cost-effective mechanization. The coding process, however, introduces phase errors whose effect must be included in the design. An approximate analysis is presented, valid for moderate to high compression ratios, which allows error effects on compressed pulse amplitude and sidelobes to be calculated in a simple manner. The anaylsis provides criteria for selecting the coding bit width (sample rate), weighting network bandwidth, and phase-coder quantization interval and transition times. Weighting functions for maximizing the signal-to-noise ratio (SNR) or for producing desired close-in sidelobe performance are derived, as is an exact expression for the transmitted spectrum. Numerical results are presented for Gaussian and the maximum-SNR weighting. The results indicate that performance will be satisfactory for many applications.